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];
plot(X,Y,'k');
xlim([-1 1]);
ylim([-1 1]);
ax = gca;
box off;
ax.Position = [0.05 0.05 0.9 0.9];
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
ax.XTickLabel = {};
ax.YTickLabel = {};
h = title('ClassicalRK4');
h.Interpreter = 'latex';
saveas(gcf,'pictures/test199/ClassicalRK199_4.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
3.13732e-07
6.56057e-09
7.33634e-10
6.03845e-11
];
T = [
12.811
23.37
43.774
86.947
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
saveas(gcf,'pictures/test199/ClassicalRK199_T.png');
figure(1);
X = [
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];
plot(X,Y,'k');
xlim([-1 1]);
ylim([-1 1]);
ax = gca;
box off;
ax.Position = [0.05 0.05 0.9 0.9];
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
ax.XTickLabel = {};
ax.YTickLabel = {};
h = title('ESDIRK6');
h.Interpreter = 'latex';
saveas(gcf,'pictures/test199/ESDIRK199_6.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
9.47984e-08
4.32149e-09
2.15757e-10
8.93553e-12
];
T = [
26.921
38.159
96.198
158.358
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
saveas(gcf,'pictures/test199/ESDIRK199_T.png');
figure(1);
X = [
0.87978
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2.04899e-05
];
plot(X,Y,'k');
xlim([-1 1]);
ylim([-1 1]);
ax = gca;
box off;
ax.Position = [0.05 0.05 0.9 0.9];
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
ax.XTickLabel = {};
ax.YTickLabel = {};
h = title('Fehlberg6');
h.Interpreter = 'latex';
saveas(gcf,'pictures/test199/Fehlberg199_6.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
9.55292e-08
1.42322e-09
8.0081e-11
1.2659e-11
];
T = [
25.741
47.256
92.488
185.103
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
saveas(gcf,'pictures/test199/Fehlberg199_T.png');
figure(1);
X = [
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0.879779
0.879778
0.879775
0.879771
0.879766
0.87976
0.879753
0.879744
0.879734
0.879723
0.87971
0.879696
0.87968
0.879662
0.879642
0.879621
0.879597
0.879572
0.879544
0.879513
0.87948
0.879445
0.879406
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];
plot(X,Y,'k');
xlim([-1 1]);
ylim([-1 1]);
ax = gca;
box off;
ax.Position = [0.05 0.05 0.9 0.9];
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
ax.XTickLabel = {};
ax.YTickLabel = {};
h = title('DormandPrince7');
h.Interpreter = 'latex';
saveas(gcf,'pictures/test199/DormandPrince199_7.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
5.51835e-08
9.78949e-10
8.70254e-11
8.34383e-12
];
T = [
36.48
65.8
123.875
229.854
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
saveas(gcf,'pictures/test199/DormandPrince199_T.png');
figure(1);
X = [
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];
plot(X,Y,'k');
xlim([-1 1]);
ylim([-1 1]);
ax = gca;
box off;
ax.Position = [0.05 0.05 0.9 0.9];
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
ax.XTickLabel = {};
ax.YTickLabel = {};
h = title('GaussLegendre1');
h.Interpreter = 'latex';
saveas(gcf,'pictures/test199/GaussLegendre199_1.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
0.00588139
0.00146587
0.000366192
9.15308e-05
];
T = [
0.821
1.636
3.016
6.425
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
figure(1);
X = [
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0.0777352
0.0764992
0.0752551
0.074003
0.0727428
0.0714746
0.0701985
0.0689145
0.0676227
0.0663232
0.0650159
0.063701
0.0623785
0.0610486
0.0597112
0.0583665
0.0570145
0.0556553
0.0542891
0.0529158
0.0515356
0.0501487
0.048755
0.0473548
0.0459481
0.0445351
0.0431158
0.0416905
0.0402592
0.0388221
0.0373794
0.0359311
0.0344775
0.0330188
0.031555
0.0300864
0.0286132
0.0271355
0.0256535
0.0241675
0.0226776
0.0211841
0.0196872
0.018187
0.0166839
0.015178
0.0136695
0.0121588
0.0106461
0.00913155
0.00761545
0.00609806
0.00457961
0.00306037
0.00154059
2.05217e-05
];
plot(X,Y,'k');
xlim([-1 1]);
ylim([-1 1]);
ax = gca;
box off;
ax.Position = [0.05 0.05 0.9 0.9];
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
ax.XTickLabel = {};
ax.YTickLabel = {};
h = title('GaussLegendre2');
h.Interpreter = 'latex';
saveas(gcf,'pictures/test199/GaussLegendre199_2.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
2.43585e-07
1.5227e-08
9.51727e-10
6.39834e-11
];
T = [
2.662
5.049
10.001
20.019
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
figure(1);
X = [
0.87978
0.879779
0.879778
0.879775
0.879771
0.879766
0.87976
0.879753
0.879744
0.879734
0.879723
0.87971
0.879696
0.87968
0.879662
0.879642
0.879621
0.879597
0.879572
0.879544
0.879513
0.87948
0.879445
0.879406
0.879365
0.879321
0.879273
0.879223
0.879168
0.87911
0.879049
0.878983
0.878914
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0.878679
0.878592
0.8785
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0.877965
0.877842
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0.877578
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0.877291
0.877139
0.87698
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0.876643
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0.87628
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0.875889
0.875684
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2.05217e-05
];
plot(X,Y,'k');
xlim([-1 1]);
ylim([-1 1]);
ax = gca;
box off;
ax.Position = [0.05 0.05 0.9 0.9];
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
ax.XTickLabel = {};
ax.YTickLabel = {};
h = title('GaussLegendre3');
h.Interpreter = 'latex';
saveas(gcf,'pictures/test199/GaussLegendre199_3.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
1.06514e-11
6.62053e-13
2.9499e-13
2.59115e-13
];
T = [
6.046
10.683
22.277
43.313
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
figure(2);
legend('s = 1','s = 2','s = 3');
saveas(gcf,'pictures/test199/GaussLegendre199_T.png');
